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In Gluon gluon production of Higgs, is it possible for higgs to decay to following channels:

  1. A pair of virtual photons which then decay to a pair of leptons each.

  2. To an on shell Z boson and a virtual photon and then each of them decays to a pair of leptons?

I am asking this question in reference to the standard model or (higgs) effective field theory for higgs to 4 lepton channel.

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Since Feynman rules feature neither a vertex $H\gamma\gamma$, nor a vertex $HZ\gamma$, what you considered requires higher-order corrections. Here is the leading-order tree diagram and the next-leading-order diagrams matching your criteria, i.e. 4 leptons in the final state, with a vertex $Z l^+l^-$ or $\gamma l^+l^-$.

enter image description here

enter image description here

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  • $\begingroup$ What if the higgs itself is off shell? $\endgroup$ – kg__ Jun 8 '17 at 21:25
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    $\begingroup$ It doesn't matter $\endgroup$ – user154997 Jun 8 '17 at 21:30
  • $\begingroup$ In the higgs to gamma gamma diagram you have shown, on including the virtual top quark or W boson loop, are the photons produced off shell? If they are on shell, I cannot get a pair of on shell leptons from them. As I want to have 4 leptons to be the final particles to get Higgs to 4 lepton channel $\endgroup$ – kg__ Jun 8 '17 at 22:01
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    $\begingroup$ The photons could be off-shell and give you 4 leptons, sure. That's a higher-order correction which may be incorporated in present theoretical predictions. I have not checked in a long while. Are you planning to compute one of those? $\endgroup$ – user154997 Jun 8 '17 at 22:08
  • $\begingroup$ Not yet, maybe later. I came across such Feynman diagrams when I generated events for higgs to 4 leptons for my Higgs EFT study. So was thinking about the validity of such diagrams. $\endgroup$ – kg__ Jun 8 '17 at 22:14

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